Exercise 1 Page 718

Recall that in a binomial experiment with n independent trials there are two possible outcomes, a success and a failure. The probability of success, which is the probability of a positive answer, equals p= 0.63. Conversely, the probability of a failure is denoted as 1- p. 1- p=1- 0.63 Now, for a binomial experiment, the probability of exactly k successes can be written with the following formula. Note that k successes is equivalent to k people saying they are sports fans. P(k successes ) = _nC_kp^k(1-p)^(n-k) In this formula, _nC_k can be expanded using a formula for the number of combinations. _nC_k ⇔ n!/k!(n-k)! Now, let's substitute n= 14 and p= 0.63 into our formula and simplify. P(k) = _(14)C_k( 0.63)^k(1- 0.63)^(14-k) ⇓ P(k) = _(14)C_k(0.63)^k(0.37)^(14-k) We need to calculate the probability of k successes for each possible value of k. Note that there can be as many as k=0,1,2,..., 14 successes in this trial. Let's use a table for this.